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Synthetic CT-enabled weekly adaptive radiotherapy for nasopharyngeal carcinoma: Optimizing plan adaptation triggers through volumetric-dosimetric monitoring. [PDF]

J Appl Clin Med Phys
Cao Z, Wu C, Han L, Duan T, Zhang F, Zhang L, Wang B, Lei W, Ni X.   +8 more
europepmc   +1 more source

Nodal Solutions for Supercritical Laplace Equations

, 2016
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Nodal Solutions of a p-Laplacian Equation

Proceedings of the London Mathematical Society, 2005
Summary: We prove that the \(p\)-Laplacian problem \(-\Delta_p u = f(x, u)\), with \(u \in W_0^{1,p}(\Omega)\) on a bounded domain \(\Omega \subset \mathbb R^N\), with \(p > 1\) arbitrary, has a nodal solution provided that \(f : \Omega\times\mathbb R \to \mathbb R\) is subcritical, and \(f(x, t) / |t|^{p-2}\) is superlinear.
Tobias Weth, Zhaoli Liu, Thomas Bartsch
exaly   +3 more sources

Solution of inverse nodal problems

Inverse Problems, 1989
We show that the coefficients in a second-order differential equation can be determined from the positions of the nodes for the eigenfunctions. We prove uniqueness results, derive approximate solutions, give error bounds and present numerical experiments.
Hald, Ole H., McLaughlin, Joyce R.
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On the Geometric Measure of Nodal Sets of Solutions

Journal of Partial Differential Equations, 1994
We present some general methods for the estimation of the local Hausdorff measure of nodal sets of solutions to elliptic and parabolic equations. Our main results (Theorems 3.1 and 4.1) improve previous results of Lin Fanghua in [1].
Han, Qing, Lin, Fanghua
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Nodal Solutions for Indefinite Robin Problems

Bulletin of the Malaysian Mathematical Sciences Society, 2017
Given a bounded domain \(\Omega \subseteq \mathbb{R}^N\) with a \(C^2\)-boundary, the authors study semilinear Robin problems of the form \[ \begin{cases} -\Delta u(z)+\xi(z)u(z) = f(z,u(z)) &\text{in }\Omega,\\ \frac{\partial u}{\partial n}+\beta(z)u=0 &\text{on }\partial \Omega, \end{cases} \] where the potential function \(\xi\) belongs to \(L^s ...
Filippakis, Michael, Papageorgiou, Nikolaos S.   +1 more
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Localized Nodal Solutions for Schrödinger-Poisson Systems

Acta Mathematica Scientia, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xing, He, Rui, Liu, Xiangqing
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Nodal solutions of -Laplacian equations

Nonlinear Analysis: Theory, Methods & Applications, 2007
The aim of this paper is to study the existence of nodal radial solutions for the \(p(x)\)-Laplacian equation of the form \[ \begin{gathered} -\text{div}(|\nabla |^{p(x)-2}\nabla u)+ a(x)|u|^{p(x)-2} u=|u|^{q(x)- 2} u\quad\text{in }\Omega,\\ u\in W^{1,p(x)}_0(\Omega).\end{gathered}\tag{1} \] Using a variational method, the authors prove that, for any ...
Fan, Xianling, Zhao, Yuanzhang
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Nodal Solutions for a Weighted (p,q)-Equation

Journal of Convex Analysis, 2022
We consider a Dirichlet problem driven by a weighted (p,q)-Laplacian with a reaction that involves a critical term and a locally defined perturbation. Using variational tools and cut-off techniques, we show that the problem has a sequence of arbitrarily small nodal solutions.
Liu, Zhenhai, Papageorgiou, Nikolaos S.
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Nodal solutions for anisotropic \((p, q)\)-equations

Nonlinear Analysis: Real World Applications, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zeng, Shengda, Papageorgiou, Nikolaos S.
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